Research interests :
I am interested in canonical or special metrics in Kähler and Sasakian geometries, including constant scalar curvature ones. I study algebraic invariants (K-stability, Futaki invariant,..) obstructing the existence of these metrics in relation with the Yau-Tian-Donaldson conjecture and also constructions of Extremal Kähler/Sasaki metrics.
Publications :
(with V.Apostolov, D.M.J. Calderbank) Weighted K-stability of polarized varieties and extremality of Sasaki manifolds, arXiv:math.DG/2012.08628. Advances in Math. 391 (2021).
(with Ruadhaí Dervan) Valuative stability of polarised varieties , arXiv:math.DG/2010.04023. Math. Ann. (2022).
Localizing the Donaldson-Futaki invariant, arXiv:math.DG/2006.08987 . International Journal of Mathematics Vol. 32, No. 08.
(with Martin de Borbon) Toric Sasaki-Einstein metrics with conical singularities, to appear in Selecta Math. arXiv:math.DG/2005.03502.
(with C. Boyer, H.Huang, C. W. Tønnesen-Friedman) Some open problems in Sasaki geometry, Australian-German Workshop on Differential Geometry in the Large, Cambridge University Press. 2020 arXiv:math.DG/1906.04827.
A note on extremal toric almost Kähler metrics, Moduli of K-stable varieties, 31, Springer INdAM Serie, (2019). arXiv:1811.05693.
(with V.Apostolov, D.M.J. Calderbank, P. Gauduchon) Levi-Kähler reduction of CR structures, products of spheres, and toric geometry, Mathematical Research Letters, Vol. 27, No. 6 (2020), pp. 1565-1629. arXiv:math.DG/1708.05253.
(with V.Apostolov, D.M.J. Calderbank, P. Gauduchon) Toric contact geometry in arbitrary codimension, arXiv:math.DG/1708.04942IMRN, Volume: 2020, Issue: 10, May 2020, pp. 2436--2467.
(with C. Boyer, H.Huang) An application of the Duistertmaat-Heckman Theorem and its extensions in Sasaki Geometry, arXiv:math.DG/1708.03006. Geometry & Topology, Volume 22, Number 7 (2018), 4205--4234.
(with Y.Rollin) Hamiltonian stationary Lagrangian fibration, hal-01332545 J. of Symplectic Geometry, 3, Volume 17 (2019) pp. 753--791.
(with C. Boyer, H.Huang, C. W. Tønnesen-Friedman) Reducibility in Sasakian geometry, arXiv:math.DG/1606.04859. To appear in Trans. of the AMS
(with C. Boyer, H.Huang, C. W. Tønnesen-Friedman) The Einstein--Hilbert functional and the Sasaki-Futaki invariant, Int.Math.Res.Not., 2017, 2017 (7), pp.1942--1974. arXiv:math.DG/1506.06084.
(with R. Sena-Dias) Toric aspects of the first eigenvalue, arXiv:math.DG/1505.01678 The Journal of Geometric Analysis, 2018, 28 (3), pp.2395--2421.
(with V. Guillemin, R. Sena-Dias) Simple spectrum and Rayleigh quotients, Contemporary Mathematics, AMS, 2015.
Toric Kähler-Einstein metrics and convex compact polytopes, Journal of Geometric Analysis, 26(1), 399--427. (arXiv:math.DG/1112.3239).
(with C. W. Tønnesen-Friedman) Toric Generalized Kähler-Ricci Solitons with Hamiltonian 2-form, Mathematische Zeitschrift, Math Z. 274 (2013), pp. 1177–1209., ou arXiv.
Existence and non uniqueness of constant scalar curvature toric Sasaki metrics, Compositio Mathematica 147 (2011), pp. 1613–1634 (ou arXiv).
Toric geometry of quadrilaterals, Journal of Symplectic Geometry 9 (2011), pp. 343–385 (ou arXiv).
Extrema of low eigenvalues for the mixed problem on the disk, Canadian Journal of Mathematics 62 (2010), pp. 808–826 (preliminary version ici).
Thesis
Doctorat (PhD) Géométrie torique des quadrilatères convexes, 2010.
UQAM (Canada) – Ecole Polytechnique (France)
Supervisor : Pr. Vestislav Apostolov (UQAM), Pr. Paul Gauduchon (X).
Maîtrise (Master) Géométrie des problèmes mixtes Dirichlet–Neumann, 2006.
Université de Montréal (Canada)
Supervisor Pr. Iosif Polterovich (UdeM).